flumefan1
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Hi, the first part of the question asks me to calculate the Maclaurin expansions of ex and ln(1+x), and verify the derivatives of the expansions are equal to ex and 1/1+x respectively.
I have done this.
The next exercise states: Use your results from the previous exercise to verify that exp(ln(1+x)) equals 1+x to the order that your expansions give you information.
What I don't get is how does the previous exercise relate to this?
Last edited by flumefan1; 1 week ago
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ghostwalker
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(Original post by flumefan1)
Hi, the first part of the question asks me to calculate the Maclaurin expansions of ex and ln(1+x), and verify the derivatives of the expansions are equal to ex and 1/1+x respectively.
I have done this.
The next exercise states: Use your results from the previous exercise to verify that exp(ln(1+x)) equals 1+x to the order that your expansions give you information.
What I don't get is how does the previous exercise relate to this?
exp is the name of the function that sends x to e^x

So, it's asking you for the expansion of e^{\ln(x+1)}

Does that cover the problem you're having?
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flumefan1
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(Original post by ghostwalker)
exp is the name of the function that sends x to e^x

So, it's asking you for the expansion of e^{\ln(x+1)}

Does that cover the problem you're having?
Yes but how do I find that expansion?
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DFranklin
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(Original post by flumefan1)
Yes but how do I find that expansion?
You have expansions (I don't know how many terms you're calculating to, so I've written ..., but stop at the appropriate power).

Exp(x) = a+bx+cx^2+... and
Ln(1+x)=A+Bx+Cx^2+... (Yes, I know A=0).

So you can set y = A+Bx+Cx^2+... and calculate Exp(y) (using your expansion for Exp and discarding terms of higher order than your original expansions), and you should get 1+x.
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flumefan1
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Thank you 😊 I shall try that in the morning and let you know how I get on.
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